Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent

Bettencourt, Joao; Lopez, Cristobal; Hernandez-Garcia, Emilio;
Journal of Physics A 46, 254022 (1-20) (2013)

In this paper we use the finite size Lyapunov Exponent (FSLE) to
characterize Lagrangian coherent structures in three-dimensional
(3d) turbulent flows. Lagrangian coherent structures act as the organizers of
transport in fluid flows and are crucial to understand their
stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields
are used to locate these coherent structures.

Three-dimensional FSLE fields are calculated in two phenomenologically
distinct turbulent flows: a wall-bounded flow (channel
flow) and a regional oceanic flow obtained by numerical solution of
the primitive equations where two-dimensional turbulence

In the channel flow, autocorrelations of the FSLE field show
that the structure
is substantially different from the near wall to the mid-channel
region and relates well to the more widely studied Eulerian
coherent structure of the turbulent channel flow. The ridges
of the FSLE field have complex shapes due to the 3d
character of the turbulent fluctuations.

In the oceanic flow, strong horizontal stirring is present and the flow regime
is similar to that of 2d turbulence where the domain is populated
by coherent eddies that interact strongly. This in turn results in the
presence of high FSLE lines throughout the domain leading to strong non-local
mixing. The ridges of the FSLE field are
quasi-vertical surfaces, indicating that the horizontal dynamics dominates
the flow. Indeed, due to rotation and stratification, vertical motions
in the ocean are much less intense than horizontal ones. This suppression is
absent in the channel flow, as the 3d character of the FSLE ridges shows.

This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Lyapunov analysis: from dynamical systems theory to applications'.

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